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> World Matrices via TiDAR Executions: 3×3×3 Parallel Triadic Computation
Coordinates multi-agent systems using GF(3) trit assignments (-1,0,+1) and conservation checks (sum ≡0 mod 3) for triadic compositions. For ALIFE diffing, counterfactual navigation, categorical rewriting.
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World Matrices via TiDAR Executions: 3×3×3 Parallel Triadic Computation
Version: 1.0.0 Trit: 0 (ERGODIC - coordinates execution) Color: #55D9A0
Worldmat is a 3×3×3 matrix of TiDAR executions where:
Each cell executes the TiDAR pattern:
TEMPORAL AXIS
PAST PRESENT FUTURE
↓ ↓ ↓
┌─────────────────────────────┐
│ ┌───┐ ┌───┐ ┌───┐ │
MINUS │ │-1 │ │ 0 │ │+1 │ ← GF(3)=0
│ └───┘ └───┘ └───┘ │
POLARITY │ ┌───┐ ┌───┐ ┌───┐ │
ERGODIC│ │ 0 │ │+1 │ │-1 │ ← GF(3)=0
│ └───┘ └───┘ └───┘ │
│ ┌───┐ ┌───┐ ┌───┐ │
PLUS │ │+1 │ │-1 │ │ 0 │ ← GF(3)=0
│ └───┘ └───┘ └───┘ │
└─────────────────────────────┘
↑ ↑ ↑
GF(3)=0 for each column
| Property | Value | Guarantee |
|---|---|---|
| GF(3) Conservation | All slices sum to 0 | Row, Column, Depth |
| SPI | Same seed → Same result | Parallel or Sequential |
| Spectral Gap | 0.25 (1/4) | Ergodic mixing |
| Cells | 27 | 3³ TiDAR executions |
# Phase 1: DIFFUSION (parallel drafting)
def diffusion_draft(self, n_tokens: int = 8):
streams = self.rng.split(n_tokens)
return [stream.next()[0] for stream in streams]
# Phase 2: AR VERIFY (sequential verification)
def ar_verify(self):
prev = self.seed
for token in self.draft_tokens:
verified = mix64(prev ^ token)
self.verified_tokens.append(verified)
prev = verified
Idle agents steal work from busy agents:
class WorkStealingScheduler:
def steal_work(self, thief: Polarity) -> Optional[TiDARCell]:
busiest = max(self.queues.keys(), key=lambda p: len(self.queues[p]))
if busiest != thief and self.queues[busiest]:
return self.queues[busiest].pop(0)
return None
wm = Worldmat(master_seed=0x87079c9f1d3b0474)
wm.execute_parallel()
acset = wm.to_acset()
# Returns: {schema, parts, subparts, metadata}
# Run demo
python worldmat.py
# Verify SPI
python worldmat.py verify
# Export ACSet
python worldmat.py acset > worldmat.json
worldmat-tidar (0) forms balanced triads:
three-match (-1) ⊗ worldmat-tidar (0) ⊗ gay-mcp (+1) = 0 ✓
spi-parallel-verify (-1) ⊗ worldmat-tidar (0) ⊗ triad-interleave (+1) = 0 ✓
tidar_streaming (-1) ⊗ worldmat-tidar (0) ⊗ gay_triadic_exo (+1) = 0 ✓
from worldmat import Worldmat
from openai_acset import build_openai_acset
# Process conversations through worldmat
wm = Worldmat(master_seed=conv_fingerprint)
wm.execute_parallel()
# Each message → cell in worldmat
# Role (user/assistant/tool) → polarity
# Time → temporal phase
# Type (obs/action/pred) → modality
from gay import SplitMixTernary
# Worldmat colors from Gay-MCP
gen = SplitMixTernary(seed=worldmat.fingerprint())
palette = gen.palette_hex(n=27) # One color per cell
| File | Purpose |
|---|---|
worldmat.py | Core implementation |
SKILL.md | This documentation |
Base directory: file:///Users/bob/.claude/skills/worldmat-tidar
This skill connects to the K-Dense-AI/claude-scientific-skills ecosystem:
general: 734 citations in bib.duckdbThis skill maps to Cat# = Comod(P) as a bicomodule in the equipment structure:
Trit: 0 (ERGODIC)
Home: Prof
Poly Op: ⊗
Kan Role: Adj
Color: #26D826
The skill participates in triads satisfying:
(-1) + (0) + (+1) ≡ 0 (mod 3)
This ensures compositional coherence in the Cat# equipment structure.